1. Field of the Invention
The present invention relates generally to scattering processes, and in particular to computation of electromagnetic scattered fields from multiple scale geometries.
2. Discussion of the Related Art
Electromagnetic scattering from rough surfaces such as the surface of the ocean plays an important role in a wide range of applications including imaging, remote sensing, and detection. The analysis of the scattering processes involved in these applications poses a rather challenging scientific problem that requires description and understanding of diffraction by complicated surfaces. Computationally, the main difficulty arises from the multiple-scale nature of the scattering surfaces, whose spectrum spans a wide range of lengthscales. A number of techniques have been developed to treat associated limiting cases. For example, the high frequency case, in which the wavelength, xcex, of the incident radiation is much smaller than the surface lengthscales can be handled by asymptotic methods such as geometrical optics or physical optics approximations. On the other hand, resonant problems where the incident radiation is of the order of the surface scale are treated by perturbation methods, typically first or second or expansions in the height, h, of the surface.
However, when a multitude of scales is present on the surface, none of the techniques described above either alone or in combination in so-called two-scale approaches is adequate. The two-scale models imply a splitting of the surface into a large scale and a small scale. Typically, a first order approximation in wavelength is used to treat the smooth components of the surface, and a first order in surface height is used to deal with the rough components of the surface. The results provided by these methods are not satisfactory precisely as a result of limitations imposed by the low orders of approximation used in both, the high-frequency approximation method and the small perturbation method.
The present invention provides a rough surface scattering method and solver for efficiently computing electromagnetic scattered fields resulting from an incident wave being reflected from a slowly varying surface (high frequency case). The claimed approach to multi-scale scattering is based on the use of expansions of high order in parameter xcex. The resulting high-order perturbation expansion approach expands substantially on the range of applicability over low order methods, and can be used in some of the most challenging cases arising in applications; A surface current is induced by the incident wave. The surface current is determined by solving a surface current integral equation. A surface current ansatz is substituted into the surface current integral equation, wherein a surface current series expansion is formed having a high frequency order. The surface current series expansion includes an oscillatory factor and surface current coefficients to be determined. An asymptotic expansion of the oscillatory integral is produced such that a Taylor series including a non-convergent integral is formed. The non-convergent integral is re-interpreted by means of analytic continuation. The re-interpreted non-convergent integral is inserted into the Taylor series to solve for the surface current coefficients. The surface current coefficients are inserted into the surface current series expansion and the surface current is obtained by summing the power series in xcex with the known surface current coefficients. Finally, the scattered field is computed based upon the solved surface current, by quadratures.